The long-term operation of CO₂ electrolyzers using membrane electrode assemblies (MEAs) is limited by challenges related to water management. However, the water balance in CO₂ electrolyzer cells still has not been fully understood, and conflicting observations have been reported in the literature. In this study, a one-dimensional non-isothermal multiphysics model of an exchange MEA CO₂ electrolyzer with a Tokuyama A201 anion exchange membrane is developed to investigate the role of different physical and chemical phenomena on the water balance. The relative contributions of these processes vary with current density and membrane transport properties, which shift the dominant water transport mechanism in the cell. Our results highlight the significant contribution of homogeneous reactions, particularly OH⁻, to the water balance across the membrane. At low currents (i < 130 mA cm⁻²), homogeneous buffer reactions dominate the water balance and result in net water production near the catalyst layer. At higher currents (i > 130 mA cm⁻²), the flux is governed by electro-osmotic drag and a temperature gradient over the cathode gas diffusion electrode (GDE) with their relative contributions depending on membrane properties. Homogeneous buffering can re-emerge as the dominant mechanism at high currents if the hydroxide ion concentration in the membrane increases, for example under CO₂-limited cathode conditions, allowing hydroxide ions to react with depleted bicarbonate near the anode.